A new polyimide has been synthesized from 3,3’,4,4’-biphenyltetracarboxylic dianhydride (BPDA) a nd 2,2’-dimethyl-4,4’-diaminobiphenyl (DMB). A high-strength, high-modulus, high-temperature fibre has been developed from this polyimide via a dry-jet wet spinning method. The tensile strength of BPDA-DMB fibres is 3.3 GPa and the tensile modulus is around 130 GPa. The compressive strength of the fibres has been investigated through a tensile recoil test (TRT), while the fibre morphology after compression has been studied via polarized light microscopy (PLM) and scanning electron microscopy (SEM). From the TRT measurements, we have observed that the compressive strength of this fibre is 665 (+/-5) MPa, which is higher than those of other aromatic polymer fibres. The effect of fibre diameter on the compressive strength of BPDA-DMB fibres is not substantial. The critical compressive strain for this fibre at which the kink bands start appearing under the observation of PLM is at 0.51-0.54%. Subglass relaxation processes have been observed and the measure of an apparent relaxation strength may serve as one of the factors which significantly affect the compressive strength of the fibres. Tensile tests of pre-compressed fibres reveal a continuous loss in tensile strength (up to 30%) with increasing the compressive strain (up to 2.6%). PLM and SEM observations show that during the compression BPDA-DMB fibres form regularly-spaced kink bands at +/-60 degrees (+/-2 degrees) with respect to the fibre axis. The kink band density initially increases with the compressive strain, and reaches a maximum at around 1.1%. Further increase of the compressive strain decreases this density due to the merge of the neighbouring bands. The size of kink bands also correspondingly increases within this compressive strain region. The morphological observation via SEM implies the existence of a skin-core structure and microfibrillar texture which are common features in polymer fibres.